$\tau$-tilting finite gentle algebras are representation-finite

Pierre-Guy Plamondon

Vol. 302 (2019), No. 2, 709–716

DOI: 10.2140/pjm.2019.302.709

Abstract

We show that a gentle algebra over a field is $\tau$-tilting finite if and only if it is representation-finite. The proof relies on the “brick-$\tau$-tilting correspondence” of Demonet, Iyama, and Jasso and on a combinatorial analysis.

Keywords

representation theory, $\tau$-tilting theory, finite representation type, gentle algebras

Mathematical Subject Classification 2010

Primary: 16G20

Secondary: 16G60

Milestones

Received: 15 November 2018

Revised: 23 March 2019

Accepted: 23 March 2019

Published: 27 November 2019